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Gambler's Fallacy
 
Description:
 
The argument assigns a probability to a random event based on the notion that the past history of that type of event has some influence on its probability or future occurrence.
 

 
Comments:
 
This fallacy includes supposing that a random event is more likely to occur because it has not happened for a long time, or less likely to occur because it recently happened, or less likely to occur because it has not happened for a long time, or more likely to occur because it recently happened. An alternative version of the fallacy (sometimes called the Lottery Fallacy) is to say that a past event must have been highly probably (or even inevitable) merely because it did in fact occur.
 

 
Examples:

"This slot machine hasn't hit a jackpot in the last hour. It should pay off big any minute now."

"Given all the logically possible combinations of which DNA molecules are capable, the odds against human life evolving are staggering. Why didn't something else evolve instead? The fact that we are here proves that humans were meant to evolve."
 

 
Discussion:

It is a matter for metaphysical speculation whether all events are caused or whether some events are truly uncaused. Whatever the outcome of that debate, it is certainly true that some events are not caused by (or are causally independent of) certain other specific events or conditions. For example, a coin toss must come up either heads or tails. The specific result is caused by the force with which the coin is flipped, the precise angle at which the coin was held, etc. However, the result is not caused by the result of the previous toss. Hence, to argue, "The last toss came up heads, so this toss will probably come up tails," is to reason on the basis of a presumed causal connection that does not exist. Bad gamblers frequently make this sort of mistake, so the fallacy of mistaking mere happenstance for a caused event has come to be known as the Gambler's Fallacy.

One form that the Gambler's Fallacy takes is to expect greater uniformity than the laws of probability actually require. It is rare to get heads five times in a row when tossing a coin, but not outside the range of expected outcomes. In any case, if I get heads four times in a row, the probability of getting a heads on the next flip is still 50/50, just as it was on the previous flips. The fact that the previous flips all came up heads does not make it more likely that the next flip will come up tails. The first example above is an instance of this sort of Gambler's Fallacy.

A second form that the Gambler's Fallacy may take is the Lottery Fallacy, which is the fallacy of trying to explain a highly improbable event when any event that might have occurred in its place would have been seen as equally improbable. For example, in a lottery in which a million tickets are sold, each ticket individually is unlikely to win. However, by the rules of the game, one ticket must win. Hence, whichever ticket wins, the winning of that ticket will be highly unlikely. Nevertheless it would be a mistake to suppose that some further explanation for the winning of that particular ticket is required. The winning of that particular ticket falls within the range of outcomes allowed within the strictures of the game, and is best described as an accidental outcome. To draw a conclusion such as, "Providence selected me to win!" or "I was born lucky," is, again, to reason on the basis of a presumed causal connection that does not exist. The second example above is an instance of the lottery fallacy.

(In the past few decades physicists have been discussing something called the Anthropic Principle, which is an attempt to "explain" some of the fundamental facts of physics by pointing out that the universe must be suitable for the development of intelligent life, since, if it were not, there would be no intelligent life in the universe to theorize about the nature of the universe. Philosophers who have commented on the Anthropic Principle generally dismiss it as an example of the Gambler's Fallacy, specifically, of the lottery fallacy.)

Of course, the occurrence of highly unusual events requires an explanation. If I am walking along the beach and find a configuration of pebbles spelling the words, "The end is near," there is no fallacy in drawing the conclusion that someone caused the pebbles to fall into that configuration. It is true that the waves may have randomly washed the pebbles into this configuration - after all, it must wash them into some configuration or other - but given the huge number of meaningless configurations compared to the tiny number of meaningful configurations, the odds of a meaningful configuration occurring are so remote as to be not worth considering. It is only good reasoning to look for explanations when something highly unusual occurs.

The Gambler's Fallacy exploits our natural (and desirable) tendency to look for explanations when something improbable takes places. However, it errs by looking for an explanation where, because of the laws of probability and the strictures of the "game," none is actually needed.
 

 
Classification: A False Cause Fallacy (a retroductive fallacy of soundness with a falsehood in the major premiss).

 
Source: Pierre Simon Laplace, Philosophical Essay on Probabilities, 1819.

 

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